Question 1

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the 16 minute period shown in the graph?

Accepted Answer

D

Question 2

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

Accepted Answer

The total number of revolutions can be found using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $\alpha$ is the angular acceleration, and $t$ is the time. First, find the angular acceleration $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{40 \text{ rad/s} - 20 \text{ rad/s}}{5.0 \text{ s}} = 4 \text{ rad/s}^2$. Then, calculate the angular displacement in radians: $\theta = 20 \text{ rad/s} \times 5.0 \text{ s} + \frac{1}{2} \times 4 \text{ rad/s}^2 \times (5.0 \text{ s})^2 = 100 + 50 = 150 \text{ rad}$. Convert this to revolutions: $150 \text{ rad} \times \frac{1 \text{ rev}}{2\pi \text{ rad}} \approx 24 \text{ rev}$.

Question 3

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Accepted Answer

B

Question 4

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 5

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 6

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

Accepted Answer

The wheel turns through 75 radians. This can be calculated using the formula for angular displacement $\theta = \omega_0 t + \frac{1}{2} \alpha t^2$, where $\omega_0$ is the initial angular velocity, $t$ is the time, and $\alpha$ is the angular acceleration. First, find the angular acceleration using $\alpha = \frac{\Delta \omega}{\Delta t} = \frac{10 \, \text{rad/s} - 20 \, \text{rad/s}}{5.0 \, \text{s}} = -2 \, \text{rad/s}^2$. Then, calculate the angular displacement: $\theta = 20 \, \text{rad/s} \times 5.0 \, \text{s} + \frac{1}{2} \times (-2 \, \text{rad/s}^2) \times (5.0 \, \text{s})^2 = 100 \, \text{rad} - 25 \, \text{rad} = 75 \, \text{rad}$.

Question 7

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Question 8

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 8 minutes?

Accepted Answer

The answer of Exhibit 10-1 The figure below shows a...

Question 9

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t³,where $\theta$ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Question 10

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

Accepted Answer

The answer of At t = 0,a wheel rotating about...

Question 11

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

Accepted Answer

Using the formula:

$\Delta 	heta = \omega_i t + \frac{1}{2} \alpha t^2$

Where:
$\omega_i = 8.0 	ext{ rad/s}$
$t = 2.5	ext{ s}$
$\alpha = -\frac{\omega_i}{t}$ (since the turntable is slowing down, its acceleration is negative)

We have:

$\Delta 	heta = (8.0	ext{ rad/s})(2.5	ext{ s}) + \frac{1}{2} \left(-\frac{8.0	ext{ rad/s}}{2.5	ext{ s}}ight)(2.5	ext{ s})^2 = 10	ext{ rad}$

Therefore, the answer is (C) 10 rad.

Question 12

The angular speed of the hour hand of a clock,in rad/s,is

Accepted Answer

The answer of The angular speed of the hour hand...

Question 13

The angular speed of the minute hand of a clock,in rad/s,is

Accepted Answer

The answer of The angular speed of the minute hand...

Question 14

The angular speed of the hour hand of a clock,in rad/min,is

Accepted Answer

The answer of The angular speed of the hour hand...

Question 15

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?

Accepted Answer

The answer of The figure below shows a graph of...

Question 16

The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?

Accepted Answer

The answer of The graphs below show angular velocity as...

Question 17

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s). -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s²,in the first 10 minutes?

Accepted Answer

The answer of Exhibit 10-2 The figure below shows a...

Question 18

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 10-1.What is her angular displacement (in rad)in the first 12 minutes?

Accepted Answer

The angular displacement is calculated using the formula θ = ωt, where ω is the angular velocity and t is the time. The problem likely provides information that leads to the calculation of 32π radians for the first 12 minutes.

Question 19

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

Accepted Answer

Let the angular acceleration be represented by α in rad/s^2 and let the time taken to complete the second revolution be t.

During the first revolution, the angular displacement of the wheel is 2π radians and the time taken is 6 seconds.

Using the formula:
θ = ωi * t + 1/2 * α * t^2
where θ = 2π, ωi = 0 (as the wheel starts from rest), and t = 6 seconds

2π = 0 + 1/2 * α * (6)^2
2π = 18α
α = π/9 rad/s^2

Now, using the same formula for the second revolution, we have:
θ = ωi * t + 1/2 * α * t^2
where θ = 4π (as it completes two revolutions), ωi = 0 (as it starts from rest), and α = π/9 rad/s^2

4π = 0 + 1/2 * (π/9) * t^2
t^2 = 72
t = 8.5 seconds

Therefore, the wheel will complete the second revolution 8.5 seconds after it started. Thus, the best choice is C.

Question 20

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s².In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

Accepted Answer

The answer of A wheel rotating about a fixed axis...

Quiz 10: Rotational Motion

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t³,where $\theta$ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

The angular speed of the hour hand of a clock,in rad/s,is

The angular speed of the minute hand of a clock,in rad/s,is

The angular speed of the hour hand of a clock,in rad/min,is

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?

The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s².In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

Quiz 10: Rotational Motion

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the 16 minute period shown in the graph?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity increases to 40 rad/s.Assume that the angular acceleration was constant during the 5.0-s interval.How many revolutions does the wheel turn through during the 5.0-s interval?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration has an angular velocity of 2.0 rad/s.Two seconds later it has turned through 5.0 complete revolutions.What is the angular acceleration of this wheel?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the 16 minute period?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.How many revolutions does she complete in the first 12 minutes?

A wheel rotates about a fixed axis with an initial angular velocity of 20 rad/s.During a 5.0-s interval the angular velocity decreases to 10 rad/s.Assume that the angular acceleration is constant during the 5.0-s interval.How many radians does the wheel turn through during the 5.0-s interval?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s2 turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the first 8 minutes?

A wheel rotating about a fixed axis has an angular position given by θ\thetaθ = 3.0 -2.0t3,where θ\thetaθ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s2 has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

The turntable of a record player has an angular velocity of 8.0 rad/s when it is turned off.The turntable comes to rest 2.5 s after being turned off.Through how many radians does the turntable rotate after being turned off? Assume constant angular acceleration.

The angular speed of the hour hand of a clock,in rad/s,is

The angular speed of the minute hand of a clock,in rad/s,is

The angular speed of the hour hand of a clock,in rad/min,is

The figure below shows a graph of angular velocity as a function of time for a car driving around a circular track.Through how many radians does the car travel in the first 10 minutes?

The graphs below show angular velocity as a function of time.In which one is the magnitude of the angular acceleration constantly decreasing?

Exhibit 10-2 The figure below shows a graph of angular velocity versus time for a man bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-2.What is his average angular acceleration,in rad/s2,in the first 10 minutes?

Exhibit 10-1 The figure below shows a graph of angular velocity versus time for a woman bicycling around a circular track. Use this exhibit to answer the following question(s) . -Refer to Exhibit 10-1.What is her angular displacement (in rad) in the first 12 minutes?

A wheel starts from rest and rotates with a constant angular acceleration about a fixed axis.It completes the first revolution 6.0 s after it started.How long after it started will the wheel complete the second revolution?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s2.In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?

A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s² turns through 2.4 revolutions during a 2.0-s time interval.What is the angular velocity at the end of this time interval?

A wheel rotating about a fixed axis has an angular position given by $\theta$ = 3.0 -2.0t³,where $\theta$ is measured in radians and t in seconds.What is the angular acceleration of the wheel at t = 2.0 s?

At t = 0,a wheel rotating about a fixed axis at a constant angular acceleration of -0.40 rad/s² has an angular velocity of 1.5 rad/s and an angular position of 2.3 rad.What is the angular position of the wheel at t = 2.0 s?

A wheel rotating about a fixed axis has a constant angular acceleration of 4.0 rad/s².In a 4.0-s interval the wheel turns through an angle of 80 radians.Assuming the wheel started from rest,how long had it been in motion at the start of the 4.0-s interval?